Witt vectors and Fermat quotient

Abstract

We give a representation of any integer as a vector of the Witt ring W(Z_p) and relate it to the Fermat quotient q(n) = (n^(p−1) − 1)/p. Logarithms are introduced in order to establish an isomorphism between the commutative unipotent groups 1+ pW(Z_p) and W(Z_p).